Abstract
We characterize a Brownian motion indexed by a semilattice of sets, using the theory of set-indexed martingales: a square integrable continuous set-indexed strong martingale is a Brownian motion if and only if its compensator is deterministic and continuous.
| Original language | English |
|---|---|
| Pages (from-to) | 903-913 |
| Number of pages | 11 |
| Journal | Journal of Theoretical Probability |
| Volume | 9 |
| Issue number | 4 |
| DOIs | |
| State | Published - Oct 1996 |
Keywords
- Compensator
- Lattice
- Set-indexed Brownian motion
- Strong martingale